The function $f(x)=\left\{\begin{matrix} \frac{|x|}{x}, & if & x≠0\\0, & if & x=0\end{matrix}\right.$ is :
Answer & explanation
Correct answer: option 2
$f(x)=\left\{\begin{matrix} \frac{|x|}{x}, &x≠0\\0, &x=0\end{matrix}\right.$
$f(x)=\left\{\begin{matrix}-1, &x<0\\0, &x=0\\1,&x>0\end{matrix}\right.$
so $LHL=-1(x=0),RHL=1(x=0)$
$f(0)=0$
discontinuous at $x=0$ $(f(0)≠LHL≠RHL)$